Fractions Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) = is parts have a dot out of Proper fraction: the top number is less than the bottom number. Ex:, 7 0, Improper fraction: the top number is equal to or is larger than the bottom number. Ex:,, 8 8 Mixed Number: a whole number is written next to a proper fraction. Ex:, 5, 0 Common Denominator: is a number that can be divided evenly by all of the denominators in the problem Ex: 8 6 Reducing Fractions to Lowest Terms The common denominator for these fractions will be. It also happens to be least common denominator. 8 6 8 8 = 6 8 Step : Find a number that goes evenly into the numerator and the denominator of the fraction. With the fraction to the left, the number that will go in evenly is 8. 6 8 = Step : Check to see whether another number goes evenly into both the numerator and denominator. Stop when there are no more numbers that can go into the fraction. In the example, the fraction can be reduced further by dividing it by. Changing Mixed Numbers to Improper Fractions Change x = 8 8 + = to an improper fraction. Step : Multiply the denominator by the whole number. Step : Add the result to the numerator. Step : Place the total over the denominator. 0/5/00 :7 Arithmetic Study Guide.doc
Adding and Subtracting Fractions With Different Bottom Numbers Example : x = x = 8 + = Example : - 6 = Step : Need to find the common denominator for all fractions. x = 6 6 x = 6 + 8 = 7 = 5 * Step : Then go ahead and add or 6-6 = subtract the fractions. 6 *Remember to change improper fractions to a mixed number. Multiplying Fractions x 5 6 = 5 5 = 5 8 Multiply the numerators across. Then multiply the denominators across. Make sure the product is in lowest terms. Multiplying with Mixed Numbers x 5 = = 8 5 = 7 5 8 7 56 = 5 5 = 5 Step : Change every mixed fraction to an improper fraction. Step : The multiply across. Step : Then, change the improper fraction to a mixed number in lowest terms. Dividing Fractions = The fraction that is right of the division sign will need to be turned upside down by writing the numerator in the denominator and the denominator in the numerator. Then follow the rules for multiplying fractions. = = = 0/5/00 :7 Arithmetic Study Guide.doc
Practice:. Change 6. 5 5 to an improper fraction.. Change 6. 5 5. to a mixed number. 6. 0 7 8 + + - - 7 7. 7 x 5 = 8. 7 x 7 =. 6 = 0. 5 5 5 6 = Answers: ) 5 6 6) 8 5 56 ) 5 8 7 7) 6 ) 8 5 ) 6 8) ) 77 5) 7 6 0) 75 0/5/00 :7 Arithmetic Study Guide.doc
Adding and Subtraction Decimals DECIMALS Add: 8.5 +.7 + 075.6 Subtract: 80.5-75 8.50 Step : Line up the decimal points. 80.5.7-75.00 + 075.60 05.5 8.57 Step : Then add or subtract. Multiplying Decimals Multiply.8 x 5.0 = 8. 50. 567 500. 5067 from the right. Dividing a Decimal by a Whole Number Step : Show the total number of places in your answer.. 07 7. 70 5 5 0 Dividing a Decimal by a Decimal Number.7.0 =. 0. 7 7. spaces Step : Multiply the decimals as you would do with whole Step : Then count the number of spaces of each factor being multiplied. Decimal places are the number of spaces to the right of the decimal point, There is in the top factor and two in the bottom factor, so the decimal is placed spaces Place the decimal point directly above its position in the problem. Then divide the same way as you divide whole numbers. Move the decimal point of the divisor (outside the bracket) as far right as you can go. Then move the decimal point in the dividend (inside the bracket) the same number of places as the divisor. Place the decimal point directly above its position in the problem. Then divide the same way as divide whole numbers. 5.8 7. 7 5 0 0/5/00 :7 Arithmetic Study Guide.doc
Practice:. 8...7. +.6 +.0 =. 8.007 +. +.0 = x.0 x 5.6 5..07 -.00 = 6. 6 -. = 7. 76. 8. 0.60. 7.055 0.8 0.. 0. 66 Answers: ) 0.7 ) 5. ).6 ) 6.57 5) 0.068 6) 5.6008 7) 6.8 8) 0.08 ) 8.5 0). 0/5/00 5:7 Arithmetic Study Guide.doc
PERCENTS Percents are used to describe a part of something. Percents are used to figure out sales or the amount of interest someone will pay on a loan. When converting a percent to its fraction form, it will always have a denominator of 00. Changing Decimals to Percents or Percents to Decimals The important key is where to move the decimal point. If changing from decimal to a percent, you would need to move the decimal point two places to the right and add the percent sign. 0.5 = 5% 0.8 = 80% To change from percent to decimal, need to move the decimal point two places to the left and drop the percent sign. 0% =. 0.% =.00 Converting Fraction to Percent Form Divide the bottom number of the fraction into the top number and move the point two places to the right. -or-. 75 00. 8 0 0 0 =.75 = 75% Multiply the fraction by 00% 5 x 00% = 75% = 75% Percent to Fraction 85% 85 00 5 5 = 7 0 Write the percent as a fraction with 00 as the denominator. Then reduce the fraction to lowest terms. Percent of a Number ) What is 5% of $6,500. ) Change the percent to a fraction n = 5% x $6,500 -or- n = (6,500) n =.5 x 6500 n = n = $,65 n =$,65 6,500 0/5/00 6:7 Arithmetic Study Guide.doc
Finding What Percent One Number Is of Another There are key words to remember that will help you solve the problem it is asking you. The word of in the sentence means to multiply. The word is means it is equal to. is what percent of 5 = a (x) 5 = 5a 5 5 The variable a is being multiplied by 5. Need to divide by 5. 5 = a 5 = a = a 5 0.0 = a 0% = a Therefore, 0% of 5 is. Finding a Number When a Percent of It is Given 0% of what number is 6?. a = 6 0 00 a = 6 6 a = 5 6 5 a = 5 5 a = 6 x 5 a = 80 Change the percent to fraction form. Need to multiply both sides of the equation by 5. Practice: Write the following in percent form.. 0.. 6 8. 5. 0. 5..5 6. What is % of $,000? 7. 60 is what percent of,000? 8. 8 is 0 % of what number? Answers: ) % ) 75% ) 0% ).% 5) 5% 6) $0 7) 0.5% 8) 70 0/5/00 7:7 Arithmetic Study Guide.doc